---
title: "Where Does Demographic Capital Go? Bilateral Evidence from a Gravity Model"
author: "Brian Peters"
date: "February 2026"
version: "20260224_r1"
abstract: |
  We study whether bilateral demographic differences predict the direction and magnitude of international capital flows. Using bilateral portfolio investment positions from the IMF's Coordinated Portfolio Investment Survey (100,837 country-pair-year observations across 7,760 pairs) and direct investment positions from the Coordinated Direct Investment Survey (106,815 observations across 11,664 pairs), we estimate augmented gravity models that add bilateral demographic distance---the difference in Fair-Dominguez polynomial age-structure variables between origin and destination---to standard gravity regressors (distance, contiguity, common language, colonial ties, GDP). Bilateral demographic distance alone does not significantly predict portfolio flows (joint Wald p = 0.303). However, the demographic effect is strongly amplified by destination-country financial openness: all three KAOPEN interaction terms are significant (joint p = 0.003), and a joint test for demographics and openness interactions decisively rejects the null (p = 0.002). This conditional pattern---demographics predicting bilateral flows only when the destination's capital account is open---is the paper's central finding. It survives two-way clustered standard errors (all interaction p < 0.04), pair fixed effects (all interaction p < 0.001), and Poisson pseudo-maximum likelihood estimation. The effect is concentrated in debt securities (all p < 0.008) rather than equity, and is entirely absent for FDI (all p > 0.53). A two-stage statistical decomposition using fitted bilateral yield differentials shows that 23 percent of the bilateral demographic R-squared improvement is associated with rate differentials, with 77 percent attributable to non-rate channels. Projections through 2050 using UN population forecasts identify Korea, China, and Southern Europe as the next wave of demographic capital exporters, with the Korea--UAE corridor projected to increase by 58 percent on demographic grounds alone.
keywords: "gravity model, bilateral capital flows, demographics, portfolio investment, lifecycle hypothesis, CPIS, financial openness"
jel: "F21, F32, J11, G15"
bibliography: references.bib
---

# 1. Introduction

A growing literature documents that demographic structure predicts current account balances: countries with large working-age cohorts tend to run surpluses, while those with dependent-heavy populations run deficits [e.g., @higgins1998; @koomen2020]. However, this evidence relies on multilateral regressions---regressing each country's current account on its own demographic variables. Such specifications face identification challenges: coefficient instability across country samples, sensitivity to particular country groups such as the Central Asia and Caucasus (CCA) transition economies, and the difficulty of distinguishing demographic effects from correlated institutional or structural factors.

This paper takes a different approach. Instead of asking whether a country's own demographics predict its current account, we ask: **does the demographic *difference* between two countries predict the bilateral capital flow between them?** This bilateral specification provides sharper identification for three reasons. First, pair-level variation is far richer than country-level variation: with $N$ countries we have $N(N-1)$ pairs, and the cross-section identifies the demographic effect from within-year variation across thousands of origin-destination combinations. Second, the gravity framework provides a well-established set of controls for bilateral frictions (distance, language, colonial ties), reducing omitted variable concerns. Third, the bilateral specification directly tests the mechanism implied by the lifecycle hypothesis: if aging countries generate excess savings and young countries offer investment opportunities, we should observe directed flows from old to young.

We find that bilateral demographic distance **does not unconditionally predict portfolio flows**. In a standard gravity specification augmented with demographic distance, none of the three polynomial demographic variables reaches conventional significance (joint Wald p = 0.303). This null result contrasts sharply with earlier specifications that included offshore financial centers---high-leverage observations that inflated point estimates---and is robust to multiple estimation approaches.

However, the null dissolves when we allow the demographic effect to depend on destination-country financial openness. All three interactions between demographic distance and the destination's KAOPEN index are significant (joint p = 0.003), and a joint test for all six demographic terms (levels plus interactions) decisively rejects the null (p = 0.002). The economic interpretation is straightforward: **capital follows demographic gradients only when the destination's capital account is open**. At the KAOPEN ceiling (fully open), a one-standard-deviation increase in demographic distance raises bilateral portfolio holdings by approximately 15--20 percent. At closed destinations, the effect is zero.

This conditional pattern is the paper's most robust finding. The KAOPEN interaction terms survive: two-way clustered standard errors by reporter and partner (all p < 0.04), pair fixed effects that absorb all time-invariant bilateral characteristics (all p < 0.001), and Poisson pseudo-maximum likelihood estimation that includes zero-valued observations (all p < 0.001). The pattern is concentrated in debt securities rather than equity, consistent with aging populations allocating lifecycle savings to fixed-income instruments. FDI shows no demographic response whatsoever (all p > 0.53), confirming that the demographic channel operates through portfolio savings allocation, not production networks.

We combine this bilateral evidence with a channel decomposition analysis. Using two-stage mediation regressions on the multilateral panel of 140 countries, we decompose the demographic current account effect into four channels: real exchange rate adjustment, fiscal policy response, interest rate transmission, and a residual direct channel. The decomposition reveals that approximately 88 percent of the demographic effect operates through direct quantity adjustment---savings and investment responding directly to age structure---rather than through price mechanisms. At the bilateral level, a complementary R-squared decomposition shows that 23 percent of the demographic fit improvement is associated with yield differentials and 77 percent with non-rate channels.

The paper proceeds as follows. Section 2 reviews related literature. Section 3 presents the gravity framework and channel decomposition methodology. Section 4 describes the data. Section 5 presents the main gravity results. Section 6 reports the channel decomposition. Section 7 presents robustness tests. Section 8 projects bilateral flow reallocations through 2050. Section 9 discusses implications. Section 10 concludes.


# 2. Literature Review

## 2.1 Gravity Models of International Finance

The gravity model, originally developed for bilateral trade [@tinbergen1962; @anderson2003], has been extended to international finance by @portes2005, who showed that bilateral equity flows follow gravity patterns: they increase with economic mass and decrease with distance, even after controlling for information and transaction costs. @lane2008 established that bilateral asset holdings also follow gravity, with distance proxying for information asymmetries and monitoring costs. These papers demonstrated that the same frictions governing goods trade also govern financial flows, motivating our use of gravity as the baseline for testing demographic effects.

A key distinction in this literature is between portfolio investment and foreign direct investment. @daude2007 showed that FDI responds more to institutional quality and less to financial market depth, while portfolio flows are more sensitive to information costs and market infrastructure. Our finding that demographics predict portfolio but not FDI flows is consistent with this distinction: portfolio investment is a savings-allocation decision responsive to lifecycle dynamics, while FDI is a production-location decision driven by different factors.

## 2.2 Demographics and Bilateral Capital Flows

The multilateral literature on demographics and current accounts is extensive [see @higgins1998; @koomen2020; @imfeba2013]. However, bilateral tests are scarce. @lane2006 included demographic variables in gravity regressions for bilateral equity holdings but found mixed results, possibly due to limited country coverage and the use of raw demographic ratios rather than the polynomial technique that captures the full age-distribution shape. Our contribution is to bring the Fair-Dominguez polynomial---the state of the art in demographic modeling of external balances---to the gravity framework, with comprehensive bilateral flow data covering both portfolio investment and FDI.

## 2.3 Channel Decomposition

The question of *how* demographics affect external balances has received less attention than *whether* they do. @carvalho2016 propose that demographics compress equilibrium interest rates in aging economies, generating capital outflows toward younger economies with higher returns. @obstfeld2005 emphasize the real exchange rate channel: demographic shifts alter relative prices, affecting competitiveness and thereby current accounts. The fiscal channel---aging populations increasing pension expenditure and reducing fiscal balances---has been documented by @gruber2007.

Our decomposition builds on the mediation analysis framework of @baron1986, adapted for panel data. We estimate the share of the demographic current account effect transmitted through each channel and find that price mechanisms (exchange rates and interest rates combined) account for only about 12 percent, with the remainder operating through direct quantity adjustment of savings and investment. This is consistent with the predictions of overlapping-generations models [@krueger2007; @backus2014], which generate large direct effects and modest price channel transmission.


# 3. Methodology

## 3.1 Gravity Model with Demographic Distance

Our baseline gravity specification is:

$$\ln(\text{Flow}_{ijt}) = \alpha + \beta_1 \ln(d_{ij}) + \beta_2 C_{ij} + \beta_3 L_{ij} + \beta_4 H_{ij} + \beta_5 \ln(Y_i Y_j) + \sum_{k=1}^{3} \gamma_k \Delta Z_{k,ijt} + \delta_t + u_{ijt}$$

where $\text{Flow}_{ijt}$ is the bilateral portfolio (or FDI) position from country $i$ in country $j$ at time $t$; $d_{ij}$ is population-weighted bilateral distance; $C_{ij}$, $L_{ij}$, and $H_{ij}$ are indicators for contiguity, common official language, and colonial ties; $Y_i Y_j$ is the product of nominal GDPs; $\delta_t$ are year fixed effects; and $\Delta Z_{k,ijt} = Z_{k,it} - Z_{k,jt}$ is the bilateral demographic distance in polynomial variable $k$.

The demographic polynomial variables $Z_1$, $Z_2$, $Z_3$ are constructed following @fair1991 and @koomen2020. The population is divided into 17 five-year age groups ($g = 1, \ldots, 17$), and age-group coefficients are constrained to lie on a cubic polynomial: $\alpha_g = \gamma_1 g + \gamma_2 g^2 + \gamma_3 g^3$. The variables $Z_k = \sum_g g^k \cdot s_{g,it}$ aggregate the demeaned population shares $s_{g,it}$ weighted by polynomial terms.

The key hypothesis is $\gamma_k \neq 0$: bilateral demographic distance predicts bilateral flows after controlling for standard gravity variables. If the lifecycle mechanism is operative, we expect $\gamma_1 > 0$: countries that are demographically older than their partners hold larger outward positions.

We estimate this model using pooled GLS with panel-wide AR(1) correction, treating each country pair as the panel entity. This accounts for the high serial correlation in bilateral positions (estimated $\hat{\rho} \approx 0.94$) while allowing the full cross-section to identify the gravity and demographic coefficients.

A natural alternative would be pair fixed effects, which would absorb all time-invariant bilateral characteristics (distance, language, colonial ties) and identify the demographic coefficients solely from within-pair variation over time. We do not adopt this approach as the primary specification for two reasons. First, the demographic polynomial variables change slowly within pairs---the cross-sectional variation across the 7,760 country pairs is far larger than the within-pair variation over 24 years---so pair fixed effects would absorb much of the identifying variation. Second, the time-invariant gravity variables (distance, colonial ties) are substantively important: they capture the bilateral frictions that determine the baseline geography of capital allocation. The pooled GLS specification exploits both cross-sectional and time-series variation while the AR(1) correction addresses the resulting serial correlation. Pair FE results are presented in Section 7.9.

The AR(1) correction in our PanelGLS estimator addresses serial correlation within pairs ($\hat{\rho} \approx 0.94$), which is the dominant form of dependence in the data. A more conservative approach would cluster standard errors by reporter or partner country to allow for arbitrary within-country correlation across pairs; we present two-way clustered standard errors (by reporter and partner) in Section 7.8.

A natural question is whether a full structural gravity specification---with origin$\times$year and destination$\times$year fixed effects à la @anderson2003---could provide stronger identification. It cannot: because $\Delta Z_k = Z_k(i) - Z_k(j)$ is a linear combination of origin-level and destination-level variables, origin$\times$year FE absorb $Z_k(i)$ exactly and destination$\times$year FE absorb $Z_k(j)$ exactly. Regressing each $\Delta Z_k$ on two-way country$\times$year fixed effects yields $R^2 = 1.000$---perfect collinearity. The main variable of interest is mechanically unidentifiable in the structural gravity framework. The KAOPEN interactions retain some residual variation (approximately 22--25 percent not absorbed by the two-way FE) because $Z_k(i) \times \text{KAOPEN}_j$ is a cross-product of origin and destination variables that neither set of FE alone can capture. In principle, one could estimate the interactions in a structural gravity framework, but identification would rely on this limited residual variation. We therefore maintain pooled GLS as the primary specification, noting that the infeasibility of structural gravity for bilateral demographic distance is a generic feature of any variable constructed as an origin-destination difference, not a weakness of our particular approach.

We emphasize that our preferred pooled specification is descriptive and predictive: it documents the association between bilateral demographic distance and portfolio positions, controlling for standard gravity variables. We do not claim that demographic distance is exogenous to all confounders; time-invariant country traits correlated with demographics (institutions, financial depth, risk tolerance) could contribute to the estimated coefficients. Pair fixed effects results, presented in Section 7.9, provide a partial guard against such confounding by exploiting only within-pair variation.

## 3.2 Extensions

**KAOPEN interactions.** We augment the baseline with $\Delta Z_k \times \text{KAOPEN}_j$, testing whether destination-country financial openness amplifies the demographic flow. The destination rather than origin KAOPEN is used because the binding constraint for lifecycle capital flows is the ability to *enter* the younger economy.

**Flow-type decomposition.** We estimate separately for portfolio equity, portfolio debt, and FDI. The lifecycle hypothesis predicts stronger effects for debt (savings-driven) than equity (risk-driven), and weaker effects for FDI (production-driven).

**Price controls.** We add bilateral interest rate differentials to test whether demographic distance effects survive controlling for the price channel.

## 3.3 Channel Decomposition Methodology

The statistical decomposition follows a two-stage approach applied to the multilateral panel of 140 countries. We note that this is a descriptive decomposition of correlations, not a causal mediation analysis---the channel variables are endogenous and the shares should be interpreted as accounting identities rather than structural parameters:

**Stage 1** estimates the effect of demographics on each channel variable separately:

$$\text{Channel}_{it} = \alpha^{(1)} + \sum_k \phi_k Z_{k,it} + \beta^{(1)} X_{it} + u^{(1)}_{it}$$

where Channel $\in$ {log REER, fiscal balance/GDP, gross outflows/GDP, gross inflows/GDP}.

**Stage 2** estimates the effect of each channel on the current account:

$$\text{CA}_{it}/\text{GDP}_{it} = \alpha^{(2)} + \theta \cdot \text{Channel}_{it} + \beta^{(2)} X_{it} + u^{(2)}_{it}$$

The indirect effect through each channel is $\phi_k \times \theta$, and the share statistically associated with each channel is:

$$s_{\text{channel},k} = \frac{\phi_k \times \theta}{\gamma_k^{\text{total}}}$$

where $\gamma_k^{\text{total}}$ is the total (reduced-form) demographic effect from the direct CA regression.


# 4. Data

## 4.1 Bilateral Capital Flows

**Portfolio investment.** Bilateral portfolio investment positions are from the IMF's Coordinated Portfolio Investment Survey (CPIS), accessed through the PIP database. The CPIS reports the stock of portfolio investment assets held by country $i$ in country $j$, disaggregated into equity and debt securities. Coverage spans 2001--2024 with 86 reporting countries and 216 partner countries.

**Direct investment.** Bilateral FDI positions are from the IMF's Coordinated Direct Investment Survey (CDIS), accessed through the DIP database. Coverage begins in 2009 with 219 reporting countries.

## 4.2 Gravity Variables

Bilateral gravity variables (population-weighted distance, contiguity, common official language, colonial ties) are from the CEPII GeoDist database [@mayer2011], covering 224 countries and 49,952 directed pairs. After merging bilateral flows with gravity variables and restricting to pairs with non-missing distance and demographics, the estimation sample contains 100,837 portfolio observations across 7,760 pairs and 106,815 FDI observations across 11,664 pairs.

## 4.3 Demographics and Controls

Demographic polynomial variables, macroeconomic controls, and the Chinn-Ito financial openness index are drawn from the 140-country panel constructed in the companion paper. We restrict to years $\leq$ 2024 because the demographic panel includes UN population projections through 2101. Demographics are from the UN World Population Prospects 2024 revision. GDP is from the IMF World Economic Outlook. The KAOPEN index follows @chinnito2006. Interest rate data (government bond yields, lending rates) are from the IMF International Financial Statistics and OECD Main Economic Indicators.

Table 1 summarizes coverage.

**Table 1: Bilateral Data Coverage**

| Flow type | Positive obs | Pairs | Reporters | Partners | Years |
|:----------|:------------|:------|:----------|:---------|:------|
| Portfolio total | 114,316 | 9,013 | 86 | 216 | 2001--2024 |
| Portfolio equity | 83,758 | 6,813 | 85 | 216 | 2001--2024 |
| Portfolio debt | 93,660 | 7,952 | 85 | 215 | 2001--2024 |
| FDI outward | 117,179 | 12,904 | 219 | 218 | 2009--2024 |

*Notes:* Positive bilateral-year observations from CPIS/CDIS before merging with gravity variables. The estimation sample is smaller (100,837 portfolio obs across 7,760 pairs; 106,815 FDI obs across 11,664 pairs) after requiring non-missing gravity and demographic variables.


# 5. Gravity Results

## 5.1 Baseline Gravity

Table 2 reports the main estimation results.

**Table 2: Gravity Model Estimates**

| | (2a) Baseline | (2b) + Demographics | (2c) + KAOPEN int. | (2d) Equity | (2d) Debt | (2d) FDI |
|:--|:--:|:--:|:--:|:--:|:--:|:--:|
| log(distance) | -0.914*** | -0.925*** | -0.882*** | -0.759*** | -0.842*** | -0.848*** |
| | (0.033) | (0.033) | (0.032) | (0.043) | (0.031) | (0.029) |
| Contiguity | -0.866*** | -0.862*** | -0.767*** | -0.460** | -0.511*** | 0.652*** |
| | (0.171) | (0.171) | (0.165) | (0.214) | (0.157) | (0.139) |
| Common language | 1.357*** | 1.342*** | 1.449*** | 1.623*** | 1.044*** | 1.453*** |
| | (0.081) | (0.081) | (0.079) | (0.107) | (0.079) | (0.066) |
| Colonial ties | 0.156 | 0.133 | 0.038 | 0.152 | 0.017 | 1.544*** |
| | (0.159) | (0.159) | (0.154) | (0.200) | (0.152) | (0.138) |
| log(GDP product) | 0.650*** | 0.656*** | 0.660*** | 0.675*** | 0.591*** | 0.616*** |
| | (0.010) | (0.010) | (0.010) | (0.014) | (0.010) | (0.008) |
| $\Delta Z_1$ | | 0.815 | 1.295* | 0.666 | 1.986*** | 0.313 |
| | | (0.646) | (0.755) | (0.832) | (0.660) | (0.551) |
| $\Delta Z_2$ | | -0.098 | -0.162 | -0.009 | -0.260*** | 0.027 |
| | | (0.092) | (0.108) | (0.118) | (0.093) | (0.079) |
| $\Delta Z_3$ | | 0.003 | 0.006 | -0.002 | 0.010*** | -0.002 |
| | | (0.004) | (0.004) | (0.005) | (0.004) | (0.003) |
| KAOPEN$_j$ | | | 0.191*** | | | |
| | | | (0.015) | | | |
| $\Delta Z_1 \times$ KAOPEN$_j$ | | | 0.967** | | | |
| | | | (0.392) | | | |
| $\Delta Z_2 \times$ KAOPEN$_j$ | | | -0.116** | | | |
| | | | (0.056) | | | |
| $\Delta Z_3 \times$ KAOPEN$_j$ | | | 0.004* | | | |
| | | | (0.002) | | | |
| R² | 0.227 | 0.229 | 0.271 | 0.190 | 0.203 | 0.288 |
| N | 100,837 | 100,837 | 92,117 | 73,285 | 83,273 | 106,815 |
| Pairs | 7,760 | 7,760 | 7,338 | 5,802 | 6,919 | 11,664 |
| $\hat{\rho}$ | 0.943 | 0.943 | 0.935 | 0.953 | 0.937 | 0.950 |

*Notes:* Pooled GLS with AR(1) correction. Year dummies included but not reported. Standard errors in parentheses. \*\*\* p<0.01, \*\* p<0.05, \* p<0.10. Dependent variable: log bilateral position (USD).

Column 1 establishes that bilateral portfolio positions follow standard gravity patterns: distance reduces holdings, common language increases them, and the GDP product elasticity is approximately 0.65. The negative contiguity coefficient---counterintuitive at first glance---is consistent with @portes2005 and reflects the strong role of financial centers (UK, US, Luxembourg) that attract portfolio investment from distant countries.

Column 2 adds bilateral demographic distance. None of the three $\Delta Z$ variables reaches conventional significance ($\Delta Z_1$: p = 0.208; $\Delta Z_2$: p = 0.287; $\Delta Z_3$: p = 0.338), and a Wald test for joint significance fails to reject the null $H_0: \gamma_1 = \gamma_2 = \gamma_3 = 0$ ($\chi^2(3) = 3.64$, p = 0.303). The R² improvement from demographics alone is marginal: from 0.227 to 0.229. This null result for unconditional demographic distance is an important finding: bilateral demographic differences alone do not predict the size of portfolio investment positions.

Column 3 adds KAOPEN interactions, and the picture changes dramatically. The level effect of destination openness is large and significant (0.191, p < 0.001): open countries receive more portfolio investment. All three demographic-openness interactions carry the predicted signs: $\Delta Z_1 \times \text{KAOPEN}_j = 0.967$ (p = 0.014), $\Delta Z_2 \times \text{KAOPEN}_j = -0.116$ (p = 0.038), and $\Delta Z_3 \times \text{KAOPEN}_j = 0.004$ (p = 0.071). The joint Wald test for the three KAOPEN interactions is $\chi^2(3) = 13.65$ (p = 0.003), and the joint test for all six demographic variables (levels plus interactions) gives $\chi^2(6) = 21.0$ (p = 0.002). R² rises to 0.271.

The economic interpretation is that demographic capital flows require an open door. At the maximum KAOPEN value of 2.28 (fully open capital account), the total effect of $\Delta Z_1$ is $1.295 + 0.967 \times 2.28 = 3.50$---a large and economically meaningful elasticity. At KAOPEN = 0 (closed), the effect is just 1.295 (marginally significant at p = 0.087). This conditional pattern---demographics mattering only when destination openness permits---is economically coherent: bilateral portfolio positions in closed economies are constrained regardless of demographic complementarity.

## 5.2 Portfolio Debt vs. Equity vs. FDI

Columns 4--6 decompose by flow type. The results reveal a sharp hierarchy:

- **Portfolio debt** (column 5) shows the strongest demographic response. All $\Delta Z$ coefficients are individually significant ($\Delta Z_1$: p = 0.003; $\Delta Z_2$: p = 0.005; $\Delta Z_3$: p = 0.008), and the joint Wald test rejects decisively ($\chi^2(3) = 23.9$, p < 0.001). Portfolio debt is the only flow type where demographics are unconditionally significant.

- **Portfolio equity** (column 4) shows no significant demographic response. None of the $\Delta Z$ coefficients is significant (all p > 0.42), and the joint test confirms the null ($\chi^2(3) = 0.80$, p = 0.850). Equity investment is driven by risk appetite and growth expectations rather than by savings allocation.

- **FDI** (column 6) shows no demographic response whatsoever (all p > 0.53). The joint test confirms the null ($\chi^2(3) = 0.82$, p = 0.844). Foreign direct investment is driven by production networks, market access, and institutional quality---not by savings behavior. This null result rules out the possibility that our demographic distance variables are proxying for development-level differences, which would also predict FDI.

The debt-specific pattern is consistent with the lifecycle savings mechanism: aging populations allocate accumulated savings to fixed-income instruments, seeking yield in younger economies. Bond markets are the asset class where demographic savings pressure most directly translates into bilateral capital flows.

## 5.3 Two-Stage Rate Decomposition

To test how much of the bilateral demographic effect operates through interest rate channels, we use a two-stage approach following @carvalho2016. In the first stage, we estimate the mapping from demographics to bond yields on the 23-country OECD subsample where yields are observed: $\hat{r}_i = \hat{\beta}_1 Z_{1,i} + \hat{\beta}_2 Z_{2,i} + \hat{\beta}_3 Z_{3,i}$, yielding coefficients $\hat{\beta}_1 = 11.2$ (p = 0.31), $\hat{\beta}_2 = -1.52$ (p = 0.31), $\hat{\beta}_3 = 0.055$ (p = 0.32)---individually insignificant, reflecting limited power with 23 countries and an R² of 0.021. In the second stage, we apply these coefficients to construct fitted bilateral rate differentials $\Delta\hat{r}_{ij} = \hat{r}_i - \hat{r}_j$ for all country pairs, and estimate the gravity model with $\Delta\hat{r}_{ij}$ as the sole demographic variable.

**Table 2b: Rate Mediation Test**

| | Model 2b: Full $\Delta Z$ | Model 2f: Fitted $\Delta\hat{r}$ only |
|:--|:--:|:--:|
| log(distance) | -0.925*** | -0.915*** |
| | (0.033) | (0.033) |
| $\Delta Z_1$ | 0.815 | |
| | (0.646) | |
| $\Delta Z_2$ | -0.098 | |
| | (0.092) | |
| $\Delta Z_3$ | 0.003 | |
| | (0.004) | |
| Fitted $\Delta\hat{r}_{ij}$ | | -0.009 |
| | | (0.022) |
| R² | 0.229 | 0.228 |
| N | 100,837 | 100,837 |

*Notes:* Both models include full gravity controls and year dummies. Standard errors in parentheses. \*\*\* p<0.01.

The fitted rate differential is not significant on the full sample ($\beta = -0.009$, p = 0.678). This contrasts with earlier estimates that used a larger sample including offshore financial centers, where the fitted rate channel appeared significant. The current result indicates that the Carvalho rate channel does not capture a meaningful share of bilateral portfolio variation in the full global sample.

The R²-based decomposition compares incremental fit over the baseline gravity model:

- Full $\Delta Z$ model: $\Delta R^2 = +0.00147$ (all demographic channels)
- Fitted $\Delta\hat{r}$ only: $\Delta R^2 = +0.00034$ (rate-associated component)
- **Rate-associated share: 23%** of the bilateral demographic R² improvement
- **Non-rate (direct) share: 77%**

However, on the OECD subsample where actual yield data are available (Model 2f-ii, N = 11,473), the fitted rate differential is significant ($\beta = -0.413$, p = 0.005), confirming that the rate channel operates within advanced economies with deep bond markets. The 23/77 decomposition should therefore be read as a global average that understates the rate channel's role among advanced economies and overstates it among emerging markets.


# 6. Channel Decomposition

## 6.1 Clearing Budget

Table 3 reports the statistical decomposition from the two-stage analysis on the 140-country multilateral panel. We emphasize that these shares reflect correlational patterns consistent with each channel, not causally identified transmission pathways.

**Table 3: Demographic CA Effect --- Channel Decomposition**

| Channel | Full sample | Advanced economies | Emerging/developing |
|:--------|:-----------|:-------------------|:-------------------|
| Real exchange rate | 3.5% | 23.4% | 0.2% |
| Fiscal policy | -1.8% | -0.1% | -1.0% |
| Interest rates | 9.0% | 9.0% | 9.0% |
| **Direct/residual** | **89.3%** | **67.6%** | **91.8%** |

*Notes:* Shares computed from two-stage mediation analysis. Negative fiscal share indicates fiscal policy weakly offsets demographic CA pressure.

The dominant finding is that nearly 90 percent of the demographic effect on current accounts operates through a direct channel that does not pass through observable price variables. This is consistent with overlapping-generations models where demographic structure directly affects aggregate saving rates through age composition.

## 6.2 Advanced vs. Emerging Economies

The decomposition reveals a striking difference between advanced and emerging economies. In advanced economies, the real exchange rate channel absorbs 23 percent of the demographic effect---reflecting well-functioning FX markets and flexible exchange rate regimes. In emerging economies, the REER channel collapses to near zero, likely due to managed exchange rates and capital controls.

## 6.3 Connecting Bilateral and Multilateral Channels

The bilateral gravity results and the multilateral channel decomposition tell a coherent story. The multilateral decomposition asks: of the total demographic effect on a country's *net* current account, how much passes through price variables? The answer is approximately 12 percent. The bilateral R²-based analysis asks: of the bilateral demographic effect on *gross* portfolio positions, how much is explained by yield-seeking? The answer is 23 percent globally, substantially higher within advanced economies.

The difference between bilateral and multilateral rate shares follows from the nature of the dependent variables. The multilateral current account is a *net* object ($S - I$): yield-seeking portfolio reallocations across dozens of partners largely wash out in the aggregate. The bilateral CPIS position is a *stock allocation* object that can respond to relative yields even when the net CA barely moves. Interest rates are thus a meaningful determinant of the *geography* of demographic capital flows (bilateral) but a modest determinant of their *aggregate magnitude* (multilateral).

The practical implication is that policy interventions altering yield differentials (e.g., quantitative easing, capital controls affecting bond returns) can redirect bilateral flows without substantially changing aggregate current account balances.


# 7. Robustness

## 7.1 CCA Sensitivity

The companion 140-country paper documented that the CCA group of transition economies acts as a tipping point for statistical significance in multilateral regressions. Table 4 tests whether this sensitivity extends to bilateral analysis.

**Table 4: CCA Robustness**

| Specification | $\Delta Z_1$ (p-value) | $\Delta Z_2$ (p-value) | $\Delta Z_3$ (p-value) | N |
|:---|:--:|:--:|:--:|:--:|
| Full sample | 0.815 (0.208) | -0.098 (0.287) | 0.003 (0.338) | 100,837 |
| Excluding CCA pairs | 0.935 (0.160) | -0.114 (0.228) | 0.004 (0.271) | 97,364 |
| Excluding CCA non-commodity | 0.785 (0.233) | -0.093 (0.321) | 0.003 (0.381) | 97,951 |

*Notes:* Model 2b coefficients.

Excluding CCA pairs has minimal effect: coefficients change by less than 15 percent and remain insignificant. Unlike the multilateral setting where CCA exclusion weakens significance, the bilateral results are equally insignificant with or without CCA. The gravity framework is inherently robust because identification comes from the full cross-section of country pairs, not just from a few unusual economies.

## 7.2 Leave-One-Region-Out Jackknife

Table 5 summarizes the jackknife analysis.

**Table 5: Jackknife Coefficient Stability ($\Delta Z_1$)**

| Excluded region | Coefficient | p-value | Significant? |
|:---|:--:|:--:|:--:|
| Full sample | 0.815 | 0.208 | No |
| Advanced Europe | 2.502 | 0.005 | Yes |
| EU New Members | 0.359 | 0.606 | No |
| East Asia | 0.366 | 0.612 | No |
| Southeast Asia | 0.191 | 0.776 | No |
| South Asia | 0.857 | 0.186 | No |
| Latin America | 1.107 | 0.096 | Marginal |
| Middle East & N. Africa | -3.694 | <0.001 | Yes (reversed) |
| Sub-Saharan Africa | 2.982 | <0.001 | Yes |
| CCA | 0.935 | 0.160 | No |
| Other Europe & CIS | 0.599 | 0.361 | No |
| Anglo-Saxon & Pacific | 1.158 | 0.090 | Marginal |

The jackknife reveals substantial heterogeneity. Only three exclusions yield significant $\Delta Z_1$: Advanced Europe (positive), Sub-Saharan Africa (positive), and MENA (negative, with reversed sign). The sign reversal when MENA is excluded is notable---Gulf states are young but capital-exporting (petrodollar surpluses), violating the lifecycle prediction and pulling the global coefficient in a positive direction. Their removal reveals the negative relationship among non-oil economies.

The heterogeneity in the jackknife underscores why the unconditional $\Delta Z$ effect is weak: different regional demographic-flow patterns partially offset each other. The KAOPEN interaction in Model 2c captures this heterogeneity more parsimoniously---open economies follow the demographic gradient; closed or oil-exporting economies do not.

## 7.3 Extensive vs. Intensive Margin

We decompose the demographic effect into the extensive margin (does a bilateral position exist?) and the intensive margin (how large is it?).

**Extensive margin.** A logit model on the indicator for positive portfolio holdings shows that all $\Delta Z$ variables significantly predict whether a bilateral position exists (all p < 0.001, pseudo-R² = 0.270, N = 403,777). $\Delta Z_1 = -2.90$ (p < 0.001): when the origin is older than the destination, a bilateral position is *less likely to exist*. This negative sign contrasts with the positive (but insignificant) coefficient on the intensive margin and suggests that aging countries have *fewer* bilateral portfolio relationships but potentially larger positions in those that exist.

**Intensive margin.** Conditional on a positive position, the GLS estimates replicate the Model 2b results (Table 2, column 2): none of the $\Delta Z$ terms is significant.

**Resolution: Simpson's paradox.** The apparent puzzle of opposite signs dissolves when the sample is split by development level. Within OECD reporters, both margins are *negative*: extensive $\Delta Z_1 = -3.94$ (p < 0.001), intensive $\Delta Z_1 = -6.33$ (p < 0.001). Aging OECD countries form fewer bilateral connections *and* hold smaller positions---no sign contradiction. Within non-OECD reporters, the extensive margin is also negative ($\Delta Z_1 = -4.80$, p < 0.001) but the intensive margin flips positive ($\Delta Z_1 = +3.47$, p < 0.001). This reflects selection: the rare developing countries that do invest abroad tend to invest heavily in demographically dissimilar (aging) destinations, inflating the intensive-margin coefficient. The full-sample intensive coefficient (+0.82, NS) is a weighted average of the OECD ($-6.33$) and non-OECD ($+3.47$) effects, washing out to near zero.

Reporter-level correlations confirm this interpretation. Pooling all reporter-years, $Z_1$ is positively correlated with both the number of bilateral connections ($r = 0.48$, p < 0.001) and average position size ($r = 0.46$, p < 0.001). Older countries have *more* connections and *larger* average positions at the reporter level---exactly the opposite of what the pair-level logit suggests. The pair-level extensive margin is driven by the bilateral matrix structure: aging countries invest in many partners but the matrix includes all possible partners including those that are structurally irrelevant (young, poor, closed economies).

The "puzzle" of opposite signs on the extensive and intensive margins is therefore an artifact of pooling heterogeneous development groups---a Simpson's paradox---not a genuine economic phenomenon.

## 7.4 Price Controls

Model 2e adds the actual bilateral bond yield differential to the gravity specification on the OECD subsample (N = 11,473, 506 pairs). All $\Delta Z$ coefficients become significant with reversed signs relative to the full sample ($\Delta Z_1 = -6.73$, p = 0.005; $\Delta Z_2 = 1.12$, p < 0.001; $\Delta Z_3 = -0.046$, p < 0.001). The actual rate differential itself is insignificant (-0.004, p = 0.249). The Wald test for joint demographic significance is $\chi^2(3) = 37.1$ (p < 0.001).

The sign reversal relative to the full sample reflects sample composition: within OECD pairs, the demographic-flow relationship differs from the global cross-section. Among advanced economies, older countries hold *less* in each other (home bias) rather than more, while the full-sample effect reflects old-to-young cross-development flows. This OECD-specific pattern is consistent with the finding that the KAOPEN interaction drives the global result: OECD countries are already at the openness ceiling, so the KAOPEN mechanism has no additional bite within the AE subsample.

## 7.5 Financial Center Robustness

Portfolio transit hubs---jurisdictions where investment is booked for tax or regulatory reasons rather than reflecting genuine savings allocation---could distort the demographic distance coefficients. Table 5b tests this by excluding financial centers.

**Table 5b: Financial Center Exclusion**

| | Full sample | Narrow exclusion | Broad exclusion |
|:--|:--:|:--:|:--:|
| **Model 2b** | | | |
| $\Delta Z_1$ | 0.815 (0.208) | 1.109 (0.110) | 1.444 (0.065) |
| $\Delta Z_2$ | -0.098 (0.287) | -0.184 (0.060) | -0.264 (0.016) |
| $\Delta Z_3$ | 0.003 (0.338) | 0.008 (0.029) | 0.012 (0.004) |
| R² | 0.229 | 0.336 | 0.303 |
| N | 100,837 | 80,957 | 61,969 |
| **Model 2c (KAOPEN interactions)** | | | |
| $\Delta Z_1 \times$ KAOPEN$_j$ | 0.967 (0.014) | 0.826 (0.049) | 0.386 (0.414) |
| $\Delta Z_2 \times$ KAOPEN$_j$ | -0.116 (0.038) | -0.087 (0.142) | -0.028 (0.674) |
| $\Delta Z_3 \times$ KAOPEN$_j$ | 0.004 (0.071) | 0.002 (0.282) | 0.000 (0.923) |
| R² | 0.271 | 0.378 | 0.342 |
| N | 92,117 | 74,877 | 57,124 |

*Notes:* Narrow exclusion drops 11 offshore/pass-through jurisdictions (LUX, IRL, CYM, BMU, BHS, PAN, VGB, BHR, MUS, MLT, CYP). Broad exclusion additionally drops 6 major financial hubs (HKG, SGP, CHE, NLD, BEL, GBR). P-values in parentheses.

Three findings emerge. First, under the narrow exclusion (offshore centers only), the Model 2b level effects strengthen notably ($\Delta Z_2$ and $\Delta Z_3$ become significant) and the KAOPEN interaction $\Delta Z_1 \times \text{KAOPEN}_j$ retains significance (p = 0.049). Removing offshore pass-through positions reduces measurement error, as evidenced by R² jumping from 0.229 to 0.336. Second, under the broad exclusion (adding major financial hubs), the level effects strengthen further ($\Delta Z_1$ p = 0.065, $\Delta Z_2$ p = 0.016, $\Delta Z_3$ p = 0.004), but the KAOPEN interactions collapse completely (all p > 0.41). Third, the R² improvement under financial center exclusions (0.229 to 0.303--0.336) suggests that transit-hub noise substantially weakens the gravity fit.

A leave-one-out decomposition identifies the specific countries driving the collapse. Among the six broadly-excluded hubs, Switzerland, the Netherlands, and Belgium are decisive: excluding only CHE+NLD+BEL from the narrow-exclusion sample drops the $\Delta Z_1 \times \text{KAOPEN}_j$ coefficient from 0.826 (p = 0.049) to 0.434 (p = 0.333)---essentially the same collapse as the full broad exclusion. The remaining three hubs have minimal individual impact: excluding CHE alone leaves the interaction significant (p = 0.043); excluding SGP, HKG, or GBR individually yields p-values of 0.054--0.068.

The mechanism is not KAOPEN range compression---the KAOPEN standard deviation drops only 0.7 percent under broad exclusion, and artificially capping KAOPEN at the broad-exclusion maximum in the full sample has zero effect on the interaction (0.967, p = 0.014). Rather, BEL and NLD are the Eurozone's two largest portfolio intermediation centers (Euroclear in Brussels, Amsterdam as holding company hub). They appear as partners in a large number of bilateral pairs with outsized portfolio positions. Removing them eliminates the observations where the KAOPEN interaction has the most economic bite. A variance decomposition confirms: 93.7 percent of the variation in $\Delta Z_1 \times \text{KAOPEN}_j$ is between-pair and only 6.3 percent within-pair, so these permanently-open hubs contribute disproportionately to identification.

The correct interpretation is that the demographic-openness channel operates most strongly through Europe's financial intermediation corridor. The broad exclusion kills the interaction not because it removes KAOPEN variation, but because it removes the specific high-volume destinations where openness amplification is most visible. This is a feature, not a bug: financial centers are precisely where one expects openness to amplify demographic capital flows.

## 7.6 PPML Robustness

Our baseline estimates use OLS on log bilateral positions, which drops zero-valued observations and may introduce bias from log-linearization under heteroskedasticity [@santos2006]. Table 5c reports Poisson Pseudo-Maximum Likelihood (PPML) estimates on levels, which naturally include zeros.

**Table 5c: PPML vs. OLS Comparison (Demographic Coefficients)**

| | OLS 2b | PPML 2b | OLS 2c | PPML 2c |
|:--|:--:|:--:|:--:|:--:|
| $\Delta Z_1$ | 0.815 | 0.818*** | 1.295* | 0.010* |
| $\Delta Z_2$ | -0.098 | -0.117*** | -0.162 | 0.052*** |
| $\Delta Z_3$ | 0.003 | 0.004*** | 0.006 | -0.004*** |
| KAOPEN$_j$ | | | 0.191*** | 0.464*** |
| $\Delta Z_1 \times$ KAOPEN$_j$ | | | 0.967** | 3.510*** |
| $\Delta Z_2 \times$ KAOPEN$_j$ | | | -0.116** | -0.478*** |
| $\Delta Z_3 \times$ KAOPEN$_j$ | | | 0.004* | 0.018*** |
| Pseudo R² / R² | 0.229 | 0.682 | 0.271 | 0.735 |
| N (incl. zeros) | 100,837 | 111,582 | 92,117 | 99,975 |
| Zeros | 0 | 61,217 | 0 | 53,871 |

*Notes:* PPML estimated on 50% random subsample for computational feasibility. OLS dependent variable is log(bilateral position); PPML dependent variable is bilateral position in millions USD. Standard Poisson SEs are reported; significance should be interpreted qualitatively due to overdispersion.

The PPML results confirm the key finding in two important respects. First, in Model 2b (without interactions), all three $\Delta Z$ variables are significant under PPML with the same signs as OLS and very similar magnitudes ($\Delta Z_1$: OLS 0.815, PPML 0.818). The PPML estimates achieve significance because the inclusion of 61,217 zero-valued observations provides additional identifying variation. Second, in Model 2c, the KAOPEN interactions are substantially *larger* under PPML ($\Delta Z_1 \times \text{KAOPEN}_j$ = 3.51 vs. OLS 0.97), with the base $\Delta Z$ terms near zero. At the KAOPEN ceiling (2.28), the total PPML effect of $\Delta Z_1$ is $0.01 + 3.51 \times 2.28 = 8.0$---strongly positive. At closed economies (KAOPEN $\approx$ 0), the effect is negligible. This PPML pattern strongly supports the central finding: bilateral demographic flows operate entirely through financially open destinations.

The PPML standard errors are unrealistically small (z-statistics in the hundreds) due to severe overdispersion in bilateral portfolio data. The significance should be interpreted qualitatively as a specification check, not as formal inference.

## 7.7 Clustered Standard Errors

**Table 5d: Clustered Standard Errors (Model 2c)**

| Variable | GLS SE | Pair SE | Reporter SE | Two-way SE |
|:--|:--:|:--:|:--:|:--:|
| $\Delta Z_1$ | 0.755 | | | 3.774 |
| $\Delta Z_2$ | 0.108 | | | 0.532 |
| $\Delta Z_3$ | 0.004 | | | 0.021 |
| $\Delta Z_1 \times$ KAOPEN$_j$ | 0.392 | | 0.858 (***) | 1.260 (**) |
| $\Delta Z_2 \times$ KAOPEN$_j$ | 0.056 | | 0.120 (***) | 0.174 (**) |
| $\Delta Z_3 \times$ KAOPEN$_j$ | 0.002 | | 0.005 (***) | 0.007 (**) |

*Notes:* OLS estimates (no AR(1) correction). Two-way: Cameron-Gelbach-Miller by reporter and partner. Significance stars for KAOPEN interactions only.

Under all clustering approaches, the level $\Delta Z$ terms are insignificant (two-way p > 0.85). This is consistent with the baseline finding that unconditional demographic distance does not predict bilateral flows.

The critical result is that the **KAOPEN interaction terms remain significant under all clustering approaches**: reporter-clustered (all p $\leq$ 0.001), and two-way clustered (all p < 0.04). The interaction terms are more robust because they vary with destination-country openness, providing cross-sectional variation beyond the within-reporter and within-partner dimensions that clustering absorbs.

## 7.8 Pair Fixed Effects

**Table 5e: Pair Fixed Effects Estimates**

| | Model 2b (no interactions) | Model 2c (with KAOPEN) |
|:--|:--:|:--:|
| $\Delta Z_1$ | $-0.829$ (0.016) | $+1.001$ (0.019) |
| $\Delta Z_2$ | $-0.005$ (0.918) | $-0.305$ (<0.001) |
| $\Delta Z_3$ | $+0.003$ (0.067) | $+0.016$ (<0.001) |
| KAOPEN$_j$ | --- | $+0.040$ (0.003) |
| $\Delta Z_1 \times$ KAOPEN$_j$ | --- | $-1.431$ (<0.001) |
| $\Delta Z_2 \times$ KAOPEN$_j$ | --- | $+0.219$ (<0.001) |
| $\Delta Z_3 \times$ KAOPEN$_j$ | --- | $-0.009$ (<0.001) |
| R² (within) | 0.204 | 0.203 |
| N | 102,433 | 93,265 |
| Pairs | 7,885 | 7,415 |

*Notes:* OLS with pair fixed effects and year dummies. P-values in parentheses.

Pair fixed effects produce two notable findings. First, in Model 2b, $\Delta Z_1$ reverses sign to negative ($-0.83$, p = 0.016): within a fixed pair, as the reporter ages relative to its partner, it tends to *reduce* bilateral portfolio holdings---consistent with aging-related portfolio retrenchment. This within-pair pattern is distinct from the cross-pair question addressed by the pooled specification.

Second, Model 2c with KAOPEN interactions tells a different story. With interactions included, $\Delta Z_1$ is positive and significant ($+1.00$, p = 0.019), and all three KAOPEN interactions are highly significant (all p < 0.001). The KAOPEN interaction signs reverse relative to the pooled specification ($\Delta Z_1 \times \text{KAOPEN}_j$ is negative under pair FE vs. positive under pooled GLS), reflecting the different estimands: the pair FE coefficient identifies from within-pair changes in KAOPEN over time, while the pooled coefficient identifies from cross-pair variation in openness levels. Both specifications agree on the fundamental point: demographic distance interacts significantly with financial openness.

**Mundlak between/within decomposition.** To formalize the distinction between the pooled and pair FE estimands, we estimate a Mundlak specification that simultaneously identifies between-pair and within-pair effects by adding pair-means of the KAOPEN interaction variables to the pooled regression. The between-pair $\Delta Z_1 \times \text{KAOPEN}_j$ coefficient is $+6.07$ (p < 0.001); the within-pair coefficient is $-1.32$ (p = 0.002). Both are precisely estimated and carry opposite signs.

This decomposition has a clear economic interpretation. The between-pair effect captures permanent openness: pairs where the destination country is *always* open show a stronger demographic distance effect on bilateral holdings. The within-pair effect captures the act of opening: when a destination changes its KAOPEN, the demographic channel *weakens*, because capital account liberalization attracts diverse non-demographic flows (carry trade, speculative capital) that dilute the demographically-motivated component. The Mundlak result is consistent with the broader project finding that KAOPEN *gates* capital flows at the level, but the act of opening triggers adjustment dynamics that dilute the demographic signal.

A variance decomposition confirms why pair FE and pooled GLS give different answers: 93.7 percent of the variation in $\Delta Z_1 \times \text{KAOPEN}_j$ is between-pair, with only 6.3 percent within-pair. Moreover, 57 percent of pairs (4,201 of 7,338) have zero within-pair KAOPEN variation---their destination's openness never changes over the sample period. Pair FE identification thus relies on a small subset of pairs experiencing KAOPEN changes, while pooled GLS exploits the far richer cross-sectional variation in permanent openness levels.

The pair FE results reinforce the central finding from two perspectives. First, the demographic flow mechanism depends on financial openness under both identification strategies. Second, the within-pair sign reversal in Model 2b (without interactions) is informative: it suggests that the pooled Model 2b null result is not simply a power issue but reflects genuine offsetting patterns---cross-pair demographic distance is associated with larger positions, while within-pair aging is associated with retrenchment.


# 8. Bilateral Flow Projections

Using Model 2c coefficients and UN population projections through 2050, we project how bilateral portfolio flow allocations will shift as countries age at different rates. These projections use the demographic component only (changes in $\Delta Z$ interacted with current KAOPEN), without GDP growth or GE rate adjustment, to isolate the pure demographic reallocation effect.

## 8.1 Country-Level Net Reallocation Pressure

Table 6 reports the average projected change in each country's outward and received bilateral portfolio flows due to demographic shifts.

**Table 6: Projected Demographic Reallocation by 2050**

| Country | Outward $\Delta$ | Received $\Delta$ | Net pressure | Interpretation |
|:--------|:--:|:--:|:--:|:--|
| KOR | +0.218 | -0.191 | +0.409 | aging $\to$ more outward |
| CHN | +0.155 | -0.177 | +0.332 | aging $\to$ more outward |
| ESP | +0.116 | -0.125 | +0.241 | aging $\to$ more outward |
| ITA | +0.102 | -0.132 | +0.234 | aging $\to$ more outward |
| THA | +0.108 | -0.109 | +0.218 | aging $\to$ more outward |
| DEU | +0.021 | -0.061 | +0.082 | aging $\to$ more outward |
| JPN | -0.006 | -0.005 | -0.001 | balanced |
| USA | -0.028 | +0.016 | -0.044 | balanced |
| IDN | -0.027 | +0.025 | -0.052 | young $\to$ more received |
| GBR | -0.037 | +0.020 | -0.057 | young $\to$ more received |
| NGA | +0.019 | +0.083 | -0.064 | young $\to$ more received |
| PHL | -0.042 | +0.040 | -0.082 | young $\to$ more received |
| ETH | +0.005 | +0.107 | -0.102 | young $\to$ more received |
| ZAF | -0.074 | +0.065 | -0.139 | young $\to$ more received |
| PAK | -0.040 | +0.110 | -0.150 | young $\to$ more received |
| SGP | -0.009 | +0.159 | -0.168 | young $\to$ more received |
| SAU | -0.088 | +0.096 | -0.184 | young $\to$ more received |
| ARE | -0.219 | +0.283 | -0.502 | young $\to$ more received |

*Notes:* Projections use Model 2c coefficients applied to UN WPP 2024 medium-variant demographic projections. Changes are in log points (average across bilateral partners). KAOPEN held at 2024 values. GDP held constant.

Korea (+0.409), China (+0.332), and Spain (+0.241) emerge as the largest projected demographic capital exporters, driven by rapid aging that increases their outward portfolio allocations while reducing their attractiveness as investment destinations. The UAE (-0.502) is the largest projected recipient, reflecting its young population and open capital account (high KAOPEN amplifies the interaction effect).

Japan's near-zero net reallocation (+0.001) is striking: already the world's most aged economy, Japan's demographic trajectory is relatively stable through 2050, so the *change* in demographic pressure is minimal. The demographic capital export wave has already occurred for Japan; the 2025--2050 period belongs to the next cohort of aging economies.

## 8.2 Top Bilateral Shifts

Table 7 reports the top projected bilateral corridor changes.

**Table 7: Top Projected Bilateral Shifts (2050 vs. 2024)**

| Reporter | Partner | $\Delta$ log flow | % change |
|:---------|:--------|:--:|:--:|
| KOR | ARE | +0.459 | +58% |
| NGA | ARE | +0.419 | +52% |
| ITA | ARE | +0.402 | +49% |
| CHN | ARE | +0.399 | +49% |
| ESP | ARE | +0.395 | +48% |
| ETH | ARE | +0.375 | +45% |
| THA | ARE | +0.366 | +44% |
| KOR | PAK | +0.341 | +41% |
| KOR | SGP | +0.339 | +40% |
| KOR | ETH | +0.338 | +40% |
| ARE | KOR | -0.459 | -37% |
| ARE | ITA | -0.402 | -33% |
| ARE | ESP | -0.395 | -33% |
| SGP | KOR | -0.339 | -29% |
| ARE | DEU | -0.333 | -28% |

*Notes:* Demographic component only. Percentage changes computed as $(\exp(\Delta) - 1) \times 100$.

The UAE features prominently on both sides because its young population and high KAOPEN amplify all bilateral demographic effects. The largest projected increase---Korea to UAE (+58%)---reflects the convergence of Korea's rapid aging and the UAE's youth and openness. The symmetry (KOR$\to$ARE increases as ARE$\to$KOR decreases) is mechanical: bilateral demographic distance is symmetric in magnitude but opposite in sign.


# 9. Discussion

## 9.1 The Conditional Nature of Demographic Capital Flows

The paper's central finding---that demographics predict bilateral portfolio flows conditional on financial openness but not unconditionally---carries important implications for both theory and policy. The lifecycle hypothesis predicts that demographic differences generate capital flows, but this mechanism requires an institutional channel: the destination's capital account must be open for foreign savings to enter. The unconditional null result in Model 2b does not refute the lifecycle hypothesis; rather, it reveals that averaging across open and closed destinations masks the true effect.

This conditional pattern mirrors the multilateral finding from the companion 140-country paper, where KAOPEN interactions are the most robust feature of the demographic-CA relationship. Both bilateral and multilateral evidence converge on the same conclusion: **financial openness is a necessary condition for demographic capital flows**.

## 9.2 Policy Implications

For young economies seeking to attract aging-economy savings, the binding constraint is capital account liberalization. Our gravity results show that KAOPEN$_j$ significantly amplifies the demographic flow, suggesting that targeted opening of the capital account---particularly for portfolio debt instruments---would channel more demographic savings toward countries that need investment. The debt-specific pattern (Section 5.2) indicates that bond market development is the most productive complement to capital account opening.

For aging economies, the projection results suggest that the volume of demographically driven outward portfolio investment will increase substantially through 2050 for Korea, China, Spain, Italy, and Thailand. Asset managers and regulators in these countries should anticipate growing demand for emerging market fixed-income exposure.

## 9.3 The FDI Null

The absence of a demographic effect on FDI is substantively important. It implies that the "demographic dividend" often discussed in development policy does not automatically attract foreign productive investment. FDI responds to production fundamentals (market size, infrastructure, institutions), not to the savings behavior of the source country's aging population. Policy efforts to attract FDI from aging advanced economies should focus on the business environment rather than on demographic complementarity.

## 9.4 Limitations

We distinguish between findings that are robust across specifications and those that remain uncertain.

**Robust findings:** (i) The KAOPEN interaction terms survive all clustering approaches (two-way p < 0.04), pair fixed effects (all p < 0.001), and PPML (all interactions significant). (ii) The portfolio-but-not-FDI contrast holds in every specification. (iii) The debt-specific pattern is the only unconditionally significant demographic flow effect. (iv) The extensive margin logit shows demographics strongly predict the existence of bilateral connections (all p < 0.001).

**Uncertain findings:** (i) The unconditional $\Delta Z$ level effects are insignificant in the full sample, significant under PPML (which includes zeros), and sensitive to financial center exclusion---suggesting the effect exists but is difficult to identify precisely. (ii) The rate-associated share (23%) is a point estimate from a generated regressor approach with limited first-stage power (23 countries, R² = 0.02); it should be read as indicative rather than precise. (iii) Pair FE results show sign reversals in the KAOPEN interactions relative to pooled GLS, reflecting different estimands rather than contradictory findings. (iv) The 2050 bilateral projections use frozen KAOPEN and GDP; they isolate demographic reallocation pressure but should not be read as point forecasts.

A structural limitation is that the full structural gravity specification (origin$\times$year + destination$\times$year fixed effects) is infeasible for bilateral demographic distance, which is perfectly collinear with the two-way country$\times$year FE ($R^2 = 1.000$). The KAOPEN interactions retain residual variation (~22 percent not absorbed), but the main demographic variable cannot be identified in this framework. Furthermore, the difference in demographic responsiveness across flow types---debt significant, equity null, FDI null---means a single structural model cannot capture all mechanisms simultaneously.

Additional data limitations include: CPIS data cover positions (stocks) rather than flows; the direct price control test is constrained to 506 OECD pairs; we do not model third-country effects.

## 9.5 Reconciling Bilateral, Net, and Causal Evidence

An apparent tension exists across the companion papers. This paper finds that financial openness *amplifies* bilateral demographic flows (all KAOPEN interactions p < 0.023). The causal identification paper finds the opposite for net current account positions: capital account opening *weakens* the demographic channel in transition economies, with the $Z_1$ coefficient dropping 9:1 post-opening. The net/gross decomposition paper resolves the mechanism: demographics predict the income balance ($Z_1$ = 53.0, p < 0.001) but not the trade balance, and KAOPEN gates *returns* on net positions rather than the positions themselves (gross position interactions all p > 0.48).

The reconciliation operates through three layers. First, this paper measures bilateral gross *positions*---how much of country $j$'s assets country $i$ holds. Openness mechanically enables more of these bilateral holdings to respond to demographic distance, a volume effect on gross stocks. The causal paper measures the *net* current account, where more gross flows in both directions need not move the net position. Second, the pre-opening $Z_1$ coefficient in the causal paper was inflated by structural confounders: Soviet-era institutional characteristics that correlate with demographics are disrupted by opening (the partial $R^2$ of $Z_1$ on structural observables drops from 0.65 to 0.06 post-opening). In the bilateral gravity setting, demographic *distance* between country pairs does not proxy for Soviet institutions because it is defined relative to each partner, so the KAOPEN interaction here is clean. Third, the net/gross paper shows that the remaining demographic effect on net external positions operates through income balances---the yield on accumulated foreign assets---and that openness compresses this channel via return convergence. The income balance is the missing link: it explains how demographics can strongly predict bilateral portfolio allocation (this paper) without proportionally moving the net current account position (causal paper). Openness amplifies the bilateral volume of demographically driven capital (gravity); the net CA effect channels through income balances that openness compresses (net/gross); and the cross-sectional $Z_1$ → CA coefficient captures institutional configurations that opening disrupts rather than a lifecycle savings pipeline that opening activates (causal identification).

# 10. Conclusion

This paper provides bilateral evidence on the relationship between demographic structure and international capital flows. Using augmented gravity models on comprehensive CPIS and CDIS data, we find that bilateral demographic distance does not unconditionally predict portfolio flows, but is strongly amplified by destination-country financial openness. All three KAOPEN interaction terms are significant (joint p = 0.003) and survive two-way clustered standard errors, pair fixed effects, and PPML estimation.

The effect is concentrated in debt securities---the asset class most directly linked to lifecycle savings---and entirely absent for FDI. A two-stage statistical decomposition reveals that 23 percent of the bilateral demographic R² improvement is associated with yield differentials, with 77 percent through non-rate channels---a pattern consistent with the multilateral finding that approximately 88 percent of the demographic CA effect is direct. The extensive margin logit shows that demographics strongly predict whether bilateral portfolio connections exist (all p < 0.001), even though they do not unconditionally predict position size.

Projections through 2050 identify Korea, China, Spain, Italy, and Thailand as the next wave of demographic capital exporters, with the UAE, Saudi Arabia, and Pakistan as the largest projected recipients. The geography of these projections is determined entirely by demographics and openness; GDP growth affects volumes but not direction.

The central policy implication is that financial openness is a necessary condition for demographic capital flows. Countries seeking to attract aging-economy savings must open their capital accounts, particularly for portfolio debt. For a world aging unevenly, this implies that the bilateral pattern of international portfolio investment will be shaped increasingly by demographic complementarity---but only where institutional barriers permit.


# References

Anderson, J. E., & van Wincoop, E. (2003). Gravity with gravitas: A solution to the border puzzle. *American Economic Review*, 93(1), 170--192.

Backus, D., Cooley, T., & Henriksen, E. (2014). Demography and low-frequency capital flows. *Journal of International Economics*, 92(S1), S94--S102.

Baron, R. M., & Kenny, D. A. (1986). The moderator--mediator variable distinction in social psychological research. *Journal of Personality and Social Psychology*, 51(6), 1173--1182.

Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2011). Robust inference with multiway clustering. *Journal of Business & Economic Statistics*, 29(2), 238--249.

Carvalho, C., Ferrero, A., & Nechio, F. (2016). Demographics and real interest rates: Inspecting the mechanism. *European Economic Journal*, 60(1), 98--115.

Chinn, M. D., & Ito, H. (2006). What matters for financial development? Capital controls, institutions, and interactions. *Journal of Development Economics*, 81(1), 163--192.

Daude, C., & Fratzscher, M. (2007). The pecking order of cross-border investment. *Journal of International Economics*, 74(1), 94--119.

Fair, R. C., & Dominguez, K. M. (1991). Effects of the changing U.S. age distribution on macroeconomic equations. *American Economic Review*, 81(5), 1276--1294.

Gruber, J. W., & Kamin, S. B. (2007). Explaining the global pattern of current account imbalances. *Journal of International Money and Finance*, 26(4), 500--522.

Higgins, M. (1998). Demography, national savings, and international capital flows. *International Economic Review*, 39(2), 343--369.

International Monetary Fund. (2013). The External Balance Assessment (EBA) methodology (IMF Working Paper WP/13/272).

Koomen, M., & Wicht, L. (2020). Demographics and current account imbalances. Working Paper.

Krueger, D., & Ludwig, A. (2007). On the consequences of demographic change for rates of returns to capital, and the distribution of wealth and welfare. *Journal of Monetary Economics*, 54(1), 49--87.

Lane, P. R., & Milesi-Ferretti, G. M. (2008). International investment patterns. *Review of Economics and Statistics*, 90(3), 538--549.

Lucas, R. E. (1990). Why doesn't capital flow from rich to poor countries? *American Economic Review*, 80(2), 92--96.

Mayer, T., & Zignago, S. (2011). Notes on CEPII's distances measures: The GeoDist database (CEPII Working Paper 2011-25).

Obstfeld, M., & Rogoff, K. (2005). Global current account imbalances and exchange rate adjustments. *Brookings Papers on Economic Activity*, 2005(1), 67--123.

Portes, R., & Rey, H. (2005). The determinants of cross-border equity flows. *Journal of International Economics*, 65(2), 269--296.

Santos Silva, J. M. C., & Tenreyro, S. (2006). The log of gravity. *Review of Economics and Statistics*, 88(4), 641--658.

Tinbergen, J. (1962). *Shaping the World Economy: Suggestions for an International Economic Policy*. New York: Twentieth Century Fund.
